使用没有高分辨率标签的物理信息卷积神经网络对流体流进行超分辨率和去噪
Super-resolution and denoising of fluid flow using physics-informed convolutional neural networks without high-resolution labels
摘要：
流体流动的高分辨率（HR）信息虽然是优选的，但由于有限的计算或实验资源，通常不太容易获得。在许多情况下，流体数据通常是稀疏的、不完整的，并且可能是有噪声的。如何提高血流数据的空间分辨率，降低噪声水平，具有重要的现实意义。深度学习（DL）技术已被证明对超分辨率（SR）任务是有效的，然而，这主要依赖于足够的HR标签进行训练。在这项工作中，我们提出了一种新的物理知情的DL为基础的SR解决方案，使用卷积神经网络（CNN），这是能够产生HR流场从低分辨率（LR）输入在高维参数空间。通过利用流体流动的守恒定律和边界条件，CNN-SR模型在没有任何HR标签的情况下进行训练。此外，提出的CNN-SR解决方案统一了物理学部分已知的情况下的正向SR和反向数据同化，例如，未知的边界条件几个流SR问题的相关心血管应用进行了研究，以证明所提出的方法的有效性和优点。高斯和非高斯MRI噪声进行了研究，以说明去噪能力。
英文摘要：
High-resolution (HR) information of fluid flows, although preferable, is usually less accessible due to limited computational or experimental resources. In many cases, fluid data are generally sparse, incomplete, and possibly noisy. How to enhance spatial resolution and decrease the noise level of flow data is essential and practically useful. Deep learning (DL) techniques have been demonstrated to be effective for super-resolution (SR) tasks, which, however, primarily rely on sufficient HR labels for training. In this work, we present a novel physics-informed DL-based SR solution using convolutional neural networks (CNN), which is able to produce HR flow fields from low-resolution (LR) inputs in high-dimensional parameter space. By leveraging the conservation laws and boundary conditions of fluid flows, the CNN-SR model is trained without any HR labels. Moreover, the proposed CNN-SR solution unifies the forward SR and inverse data assimilation for the scenarios where the physics is partially known, e.g., unknown boundary conditions. Several flow SR problems relevant to cardiovascular applications have been studied to demonstrate the proposed method's effectiveness and merit. Both Gaussian and non-Gaussian MRI noises are investigated to illustrate the denoising capability.
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